The pazer is a weaker divider than the pashta, so all of the pazer notes are part of a longer phrase that ends at the word פְּלָאיָה֙, which is marked with a pashta. (In this case there is also a dividing munach legarmeh on וְשֵׁרֵ֥בְיָ֣ה ׀ in the middle.)
וְיֵשׁ֡וּעַ וּבָנִ֡י וְשֵׁרֵ֥בְיָ֣ה ׀ יָמִ֡ין עַקּ֡וּב שַׁבְּתַ֣י ׀ הֽוֹדִיָּ֡ה מַֽעֲשֵׂיָ֡ה קְלִיטָ֣א עֲזַרְיָה֩ יֽוֹזָבָ֨ד חָנָ֤ן פְּלָאיָה֙
This isn't unusual for a verse of this length. The reason why it isn't common is because usually, lists of names are divided into multiple verses. The 13 names of 1 Chronicles 1:1-4 are spread out across four verses, so there is no division necessary beyond the tipcha of each verse:
א אָדָ֥ם שֵׁ֖ת אֱנֽוֹשׁ׃ ב קֵינָ֥ן מַֽהֲלַלְאֵ֖ל יָֽרֶד׃ ג חֲנ֥וֹךְ מְתוּשֶׁ֖לַח לָֽמֶךְ׃ ד נֹ֥חַ שֵׁ֖ם חָ֥ם וָיָֽפֶת׃
On the other hand, the verse in Nehemiah also has 13 names, but they only take up part of one verse, so more subdivisions are necessary.
Since there are no dividers weaker than a pazer, long series of names in one verse usually end up with a series of pazer, sometimes followed by telisha gedola, azla/geresh/gershayim, and/or munach legarmeh, before the next divider (either pashta, zarka, tevir, or revi'i).